A federal appeals court dealt another blow to a lawsuit targeting Maine’s COVID-19 vaccine mandate for health care workers, resulting in an 11th-hour appeal to the U.S. Supreme Court on Wednesday.

A three-judge panel of the 1st U.S. Circuit Court of Appeals declined to stop the vaccine requirement, saying a lawsuit brought by opponents of the mandate was unlikely to succeed. The state is due to begin enforcing the vaccine requirement on Oct. 29.

The decision was dated Tuesday, the same day the U.S. Supreme Court declined an emergency request to intervene.

But the Supreme Court left open the door for another appeal, and lawyers swiftly filed a request for a preliminary injunction Wednesday after the appeals court issued its final decision.

Democratic Gov. Janet Mills praised the decision by the appeals court, saying Wednesday that vaccinations “are the best tool we have to protect the lives and livelihoods of Maine people.”

“This rule protects health care workers, their patients and our health care capacity in the face of this deadly virus. Just as vaccination defeated smallpox and vaccination defeated polio, vaccination is the way to defeat COVID-19,” she said in a statement.

The 1st Circuit decision came a week after a federal judge in Maine upheld the vaccination mandate for health workers.

“Maine’s interest in safeguarding its residents is paramount. While we do not diminish the appellants’ liberty of conscience, we cannot find, absent any constitutional or statutory violation, any error in the district court’s conclusion that the rule promotes strong public interests and that an injunction would not serve the public interest,” the 1st Circuit wrote.

The Liberty Counsel, which filed the lawsuit in federal court in Maine, claims to represent more than 2,000 health care workers who don’t want to be forced to be vaccinated.

Mat Staver, founder and chair of the Liberty Counsel, said Wednesday that it’s now up to the Supreme Court “to obtain relief for these health care heroes against Governor Janet Mills’ illegal edict.”

Most health care workers have complied but several dozen have opted to quit over the mandate, and Central Maine Medical Center in Lewiston already curtailed some admissions because of a shortage of nurses. Nearly 97% of Maine emergency medical workers are vaccinated against COVID-19, Maine Department of Public Safety said Wednesday.

State agencies vowed to work with hospitals and nursing homes individually to address issues. That includes working with the facilities on recruitment and retention of workers, said Jeanne Lambrew, commissioner of the Maine Department of Health and Human Services.

“We have seen significant improvements in the vaccine rates in our hospitals and long-term care facilities,” she said.